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Causality and Relativity in Quantum Physics

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Causality and Relativity in Quantum Physics Johan F. Prins Department of Physics, University of Pretoria, Gauteng, South Africa Postal address directly to author: P O Box 1537, Cresta 2118, Gauteng, South Africa Telephone: +27 11 477-8005 Facsimile: +27 11 477-3709 e-mail: [email protected] Abstract It is argued here that the Copenhagen interpretation of quantum mechanics violates the tenets on which both Galileo’s and Einstein’s theories of relativity are based. It is postulated that the “building blocks” of the universe are not particles but are holistic wave-entities which act and interact with other wave-entities as one would expect from waves: i.e. they can change their shape and spatial extent (morph) when the boundary conditions change, and they can superpose when sharing the same region of space. It is concluded that there are two distinctly different ways in which superposition can occur: (i) the holistic waves can add without totally losing their separate identities so that the superposed wave can experience interactions between its sub-components (it is suggested that this process should be termed “enmeshment”); (ii) the holistic waves can add to completely lose their separate holistic identities in order to form a wave which is again a single holistic entity (it is suggested that this process be termed “entanglement”). A parameter is derived which defines an interface between quantum mechanics and classical mechanics: the one does not encompass the other; both are valid within their respective domains. Using this framework, a possible causal interpretation is developed for quantum mechanics which can be visualised; even the “spooky action at a distance” that worried Einstein so much, seems to follow logically. This analysis suggests a new approach to model the electron (and other fundamental particles) quantum-mechanically. The electromagnetic quantum-energy of a solitary electron does not form a field around the electron in three-dimensional space, but is finite and localised so that it is equal to the mass of the electron. An energy component along the fourth dimension is derived for the electron which could be part of the dark energy of the Universe and which, in turn, causes vacuum-energy fluctuations through Heisenberg’s uncertainty relationship for energy and time. The possible consequences of this approach are analysed and discussed. Keywords: quantum mechanics, Copenhagen interpretation, Causality, relativity. 1 Contents 1. Introduction 2. Relativity 3. Time-independent wave-functions of an electron 4. Traditional modelling of a “free” electron 5. The “path” of an electron in space 6. Heisenberg’s “uncertainty” relationship 7. Free-electron localisation 8. A two-dimensional analogue 9. Separation of matter from antimatter? 10. The essence of an electron-wave 10.1 Covalent bonding 10.2 The Mott transition 10.3 Gaussian waves 10.4 Outside the critical radius 11. Visualising quantum-mechanical interactions 11.1 Quantum jumps of an atomic electron 11.2 Interactions between atomic orbitals 11.3 The photo-electric effect and Compton scattering 11.4 Diffraction of photons and electrons 11.5 EPR experiments 11.6 Laser beams 12. Blackbody radiation 12.1 Cavity radiation 12.2 Cosmic background radiation 13. Bands and bonds in solids 14. Aspects when modelling the electron 14.1 The electric self-energy field 14.2 The Dirac equation 14.3 Which wave equation for a free electron? 14.4 The fourth dimension – dark energy? 14.5 Electron spin 14.6 Free positrons 14.7 Excited electrons 15. Nucleon bonding – nature’s single force? 16. Macro-entanglement of matter 16.1 Can matter macro-entangle? 16.2 An experiment with electrons 16.3 An experiment with buckey balls 16.4 Dark matter? 17. Creation of the universe – bending space? 17.1 Four-dimensional space, time, temperature and entropy 17.2 Alpha and omega 18. Summary and conclusion 2 1. Introduction General relativity explains big things, quantum mechanics explains little things, and if the twain meets it is on a scale that is physically undetectable and hence empirically irrelevant. Freeman Dyson as quoted in New Scientist The unpredictable, random element comes in only when we try to interpret the wave in terms of the positions and velocities of particles. But maybe that is our mistake: maybe there are no particle positions and velocities of particles, but only waves. Stephen Hawking in “A Brief History of Time” Notwithstanding opposition from formidable scientists like Einstein, Schrödinger, de Broglie and Bohm, the Copenhagen interpretation of quantum mechanics still reigns supreme after its inception 80 years ago. It is at present generally believed that realism in science has been defeated; the quantum world does not exist unless one looks for it, and in this process one becomes a creator of the “reality” one experiences. This interpretation rests primarily on two principles postulated by Born and Heisenberg, and further “rationalised” by Bohr when he formulated his principle of complementarity according to which the particle and wave behaviour are two aspects of the same “reality” which cannot manifest simultaneously: (i) According to Born the intensity of the wave-function, derived from the Schrödinger equation, is not the intensity of a “real matter wave” but a probability distribution representing the spread in possible positions at which a quantum particle (like an electron) will be found when a measurement is made. (ii) According to Heisenberg there are inbuilt uncertainties in nature. When, for example, measuring position and momentum, uncertainties must appear even if perfect measurements were possible; i.e. in terms of Planck’s reduced constant there exists along any direction in space a relationship between the uncertainty ∆r in position and ∆p in momentum of a particle; namely ∆r∆p ≥ ½ h (1) This relationship implies that the product of ∆r with ∆p can at best be equal to ½ h . In terms of the Born-interpretation, it implies that an accurate measurement of the position of a particle along the direction r, must lead to an infinitely large uncertainty in the momentum and vice- versa. 3 These two principles logically lead to the conclusion that the position and momentum of a quantum particle cannot manifest in such a way that both can be measured or known simultaneously, and that repeated measurements of any one of these parameters under exactly the same physical conditions give different results for each measurement; i.e. “God plays dice!”. The Copenhagen interpretation has become entrenched in the scientific world. In fact, it has become dangerous to advocate an objective reality for the quantum world. It is nowadays widely believed that if one attempts to do so, it implies that one does not “understand” quantum physics. In 1935 Einstein took a “last stand” against the Copenhagen interpretation when he, Podolsky and Rosen formulated their (EPR) paradox [1]. The experiment is based on the concept of “entanglement” of particles. Schrödinger coined the term “entanglement” when particles are represented by a single multi- particle wave-function. It implies an instantaneous “understanding” between the particles when they are modelled by quantum mechanics; a “spooky action at a distance”. Einstein et al pointed out that this implies that two “entangled” particles separated by light years must still be able to communicate instantaneously with each other when a measurement is made on one of them. The other particle must then “immediately” manifest an outcome that is determined by the outcome of the measurement on its partner light years away. Einstein et al reasoned that (according to Einstein’s theory of relativity) faster-than-light communication is not possible between two such particles, and therefore the instantaneous communication required by entanglement must indicate that the theory of quantum mechanics is incomplete. In 1964 John Bell derived a condition that has to be violated if such instantaneous communication can manifest [2]. Subsequent experiments on entangled photons violated Bell’s inequality [3]. This has led to the conclusion that “Einstein has been proved wrong”; our universe is indeed the bizarre, non-causal, statistical concoction portrayed by the Copenhagen interpretation. In this publication it will be argued that the Copenhagen interpretation violates fundamental relativistic concepts (from Galileo to Einstein), and that this has led to the present conundrums in physics; i.e. when a quantum “particle” with mass is analysed within its correct relativistic context it is found that a causal interpretation for quantum mechanics must apply. 2. Relativity When talking about relativity Einstein’s name immediately comes to mind; however, the real father of relativity is Galileo. He was first to consider the implications when bodies move relative to one another. He concluded that there is no mechanical experiment that one can do to determine whether you (the observer) and the “stationary surroundings” you observe around you are moving or not moving with a constant speed. From this he postulated that the earth is moving and nearly lost his life for parting with accepted scientific dogma. Galileo’s conclusions about relativity later became formalised in Newton’s first law of classical mechanics. For the purposes of this publication, Newton’s first law will be restated as follows: a body with mass that moves with a constant velocity is a “stationary body”; this is so because one can attach a 4 reference frame to such a body (its proper reference frame) within which it will be observed as being stationary and within which, according to Galileo, it will act like a “real” stationary body. The body’s mass can then be interpreted as its “inertia”; i.e. its “resistance against being moved” from its stationary position within its proper reference frame. It is well-known that it is for this reason that reference frames which move with constant velocities relative to each other have become known as “inertial” reference frames.
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